I don't know, I think the situation is weird, but I think it might be whatever reason they had they were not comfortable sharing it with you. Either she had a medical or embarrassing situation and her mom got her out of it or the mother freaked out about something or a combo.
Maybe your husband tried to reassure them that the roommate could help out more than you think he did. Maybe just to make her feel better if she was nervous about watching 3 kids all at once. So they figured that made it okay to leave the baby with him for just 20 minutes??
Some other things that came to my mind:
So they asked about guns specifically and then the roomate was playing some type of combat game?? (Isn't that game a war game?)
It IS, imo, understandable to be concerned if there is going to be a babysitter in the house AND yet another adult (especially male) is in the house (such as your roommate). Now, you were clear about it, yes, and they knew, but just pointing that out because it just something that could be part of the equation.
If I were watching 2 older children and a young one, I would feel more reassured to have a friend help me, at 19. Not all 19 year olds are great at babysitting. I also don't have siblings, so dealing with 3-- I would have only done something like that if I thought a friend could help. And I'd be unhappy if my friend couldn't do it, but I would still feel obligated to keep the job and make the best of it.
It was awkward for the 19 year old to have a misunderstanding that the roommate she was trying to communicate with was on headphones and hadn't been hearing her when she had been talking to him. My dh plays games, he sometimes wears headsets... it took me a while to get used to it = I can see that being awkward
On the one hand you HAVE to listen to your gut feeling. Maybe she's really fine, a nice girl, sweet, even good with kids but not a sitter that can handle an emergency- so not one you really want. On the other hand, she's young-ish and had to deal with a situation that might have been a little outside of her comfort level and just a little odd. And IF her mom is being a helicopter parent than maybe she has some learning to do before she can break from that and rely on herself more.
If even after all this you feel like you 'like' the girl or the mom- maybe an opportunity will come up where you can gently pry or express concern. I'd imagine if there was a legitimate excuse, they are probably thinking how awkward the situation was but also are a little embarrassed to just bring it up. Especially if the girl is immature, or her mother IS too protective-- she's not really going to know how to discuss this with you in a healthy way.